Tauberian theorems for the statistical deferred Cesàro summability of sequences of fuzzy numbers

Abstract

UDC 517.521

We introduce the concept of statistical deferred Cesàro summability for sequences of fuzzy numbers and examine its fundamental properties within the framework of fuzzy number spaces. It is shown that every bounded and statistically convergent sequence is statistically deferred Cesàro summable to the same fuzzy number provided that the deferred Cesàro mean is properly deferred, thus showing that this summability method agrees with statistical convergence. However, the converse of this statement is, in general, not true. This means that additional conditions are required for the statistical convergence to follow from the statistical deferred Cesàro summability. Furthermore, we establish necessary and sufficient Tauberian conditions under which the statistical convergence of a certain subsequence of a sequence of fuzzy numbers follows from its statistical deferred Cesàro summability. Unlike the existing Tauberian results for the Cesàro summability of fuzzy numbers, the present work deals with the statistically deferred framework, which requires the use of essentially different techniques.